Putnam 1947 B3

Let $x, y$ be Cartesian coordinates in the plane. $I$ denotes the line segment $1 \leq x \leq 3, y=1$ . For every point $P$ on $I$ , let $P^{*}$ denote that point that lies on the segment joining the origin to $P$ and such that the distance $P P^{*}$ is equal to $1 / 100$ . As $P$ describes $I$ , the corresponding point $P^{*}$ describes a certain curve $C^{*}$ . Let $l(I), l\left(C^{*}\right)$ be the lengths of $I$ and $C^{*}$ respectively. Which one of $l(I), l\left(C^{*}\right)$ is greater? Prove your answer.

Dataset text PutnamGAP. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.